Volume and Surface Area problems
- 1. If the radius of base and height of a cone are increased by 10%, find the percentage of increase of its volume
Options- A. 33.5%
- B. 33.1%
- C. 32.1%
- D. 53.1% Also asked in: Bank Exams, Bank PO
Correct Answer: 33.1%
Explanation:
v1=
v2=
% Increase in volume = (V2-V1) / (V2*100)
- 2. A single pipe of diameter x has to be replaced by six pipes of diameters 12 cm each. The pipes are used to covey some liquid in a laboratory. If the speed/flow of the liquid is maintained the same then the value of x is ?
Options- A. 14.69 cm
- B. 29.39 cm
- C. 18.65 cm
- D. 22.21 cm Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 29.39 cm
Explanation:
Volume of water flowing through 1 pipe of diameter x = Volume discharged by 6 pipes of diameter 12 cms.
As speed is same, area of cross sections should be same.
Area of bigger pipe of diameter x = Total area of 6 smaller pipes of diameter 12
i.e
Here R = R and R1 = 12/2 = 6
R = 14.696
=> D = X = 14.696 * 2 = 29.3938 cm.
- 3. Find the ratio of the surfaces of the inscribed and circumscribed spheres about a cube.
Options- A. 1:2
- B. 1;3
- C. 1:4
- D. 1:5 Also asked in: Bank Exams, Bank PO
Correct Answer: 1:2
Explanation:
- 4. The volume of a rectangular solid is to be increased by 50% without altering its base. To what extent the height of the solid must be changed.
Options- A. 50%
- B. 40%
- C. 30%
- D. 20% Also asked in: Bank Exams, Bank PO
Correct Answer: 50%
Explanation:
Let l, b the sides of the base, so that the area of the base = lb
remains constant.
Let ?h? be the height of the solid.
Volume of the solid, V = l× b× h.
Since the volume is to be increased by 50%
- 5. A store owner is packing books into larger boxes that measure 25 by 42 by 60 inches. If the measurement of each book is 7 by 6 by 5 inches, then how many books can be placed in the box ?
Options- A. 175
- B. 345
- C. 265
- D. 300 Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 300
Explanation:
Number of books that can be placed in the larger box is given by Volume of Box / Volume of book.
Now, n = 25 x 42 x 60 / 7 x 6 x 5
= 63000 / 210
= 300.
Therefore, 300 books can be in that box.
- 6. How many squares with sides 1/2 inch long are needed to cover a rectangle that is 4 ft long and 4 ft wide ?
Options- A. 9216
- B. 10246
- C. 12345
- D. 7527 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 9216
Explanation:
It takes four of those little squares -- each one 1/2 inch on a side -- to cover one square inch. That's because each one is 1/2 x 1/2, or 1/4 of a square inch.
In a rectangle that is 48 inches by 48 inches, there are 2304 square inches.(1 ft = 12 inches)
Since it takes 4 little squares to cover 1 sq inch, then it would need 2304 x 4 squares (1/2 inch on a side each) to cover a rectangle 4 feet by 4 feet.
That is 9,216 of those squares.
- 7. 88 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be ?
Options- A. 112 mts
- B. 84 mts
- C. 96 mts
- D. 108 mts Also asked in: CAT, Bank Exams, AIEEE, Bank Clerk
Correct Answer: 84 mts
Explanation:
Vol of silver = = 66 C.C
Given D= 1mm => R = D/2 = 1/20 cm
=> = 66
= 66 x 400 x (7/22) = 8400 cm = 84 mtrs.
- 8. A rectangular block has the dimensions 5x6x7 cm it is dropped into a cylindrical vessel of radius 6cm and height 10 cm. If the level of the fluid in the cylinder rises by 4 cm, What portion of the block is immersed in the fluid ?
Options- A. 22/7 x 24/35
- B. 22/7 x 36 x 4
- C. 22/7 x 36/5
- D. 22/7 x 37/21 Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 22/7 x 24/35
Explanation:
Since level of water increased in cylinder by height 4.
This is because of the rectangular block .
Therefore , area of rectangular block immersed in water is
=
Thats why portion of block immersed in water is
= (22/7 * 36 * 4) / total vol. of rectangle
= (22/7 * 36 * 4)/ (7*5*6)
= (22/7 * 24)/ 35.
- 9. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
Options- A. 84
- B. 90
- C. 168
- D. 336 Discuss
Correct Answer: 84
Explanation:
Let the length of the wire be h.
Radius r =1/2 mm = 1/20 cm
=> h= (66 x 20 x 20) x (7/22) = 8400cm = 84m
- 10. What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
Options- A. 344.35 sq.cm
- B. 462 sq.cm
- C. 498.35 sq.cm
- D. None of these Discuss
Correct Answer: 498.35 sq.cm
Explanation:
h = 14 cm, r = 7 cm.
So, l =
Total surface area = =
=
= (3.236 x 154) sq.cm
= 498.35 sq.cm
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